UNIT 2 Decimal Fractions

Key Terms Continuing number Decimal Decimal fraction Decimal place Decimal system Multiplier

Understanding Decimal Fractions

Reading Decimals (continues) Decimal Read as 0.1 One tenth 0.01 One hundredth 0.001 One thousandth 0.0001 One ten-thousandth 0.00001 One hundred-thousandth 0.000001 One millionth (continues)

Reading Decimals When reading a whole number and a decimal fraction, the decimal point is read as “and” or “point” Example: 1.5 = One and five tenths It is a good practice to place a zero (0) before the decimal point when using decimal fractions Example: 0.75 (continues)

Reading Decimals Note place value of decimal point Example: 0.67 Read number to right of decimal point Example: sixty-seven Use the name that applies to the decimal place of last number Example: sixty-seven one hundredths

Power of 10 Process of multiplying tens together Number of tens determines the power All decimals are fractions with denominator of 10 or power of 10

Common to Decimal Fractions Divide denominator into numerator Place decimal point after numerator Place decimal point in quotient directly over decimal point in numerator Place 0 after decimal point in numerator Divide, placing 0 before decimal point in quotient

Check Your Work Always double-check the accuracy of your work by multiplying the quotient by the denominator (divisor) This should give you the same number as your numerator (dividend)

Decimal to Common Fractions Read decimal fraction aloud Numerator is number to right of decimal Denominator is number of decimal places, expressed by power of 10 Reduce to lowest terms

Adding Decimals Arrange numbers in column Line up decimal points Add numbers as you would whole numbers Place decimal point directly under decimal points in problem

Reminder! When adding or subtracting decimals, you may use a zero (0) after the last digit to help you form even columns Example: 0.125 + 0.14 = _____ 0.125 + 0.140 0.265

Subtracting Decimals Arrange numbers in column Line up decimal points Subtract numbers as you would whole numbers Place decimal point directly under decimal points in problem

Multiplying Decimals Multiply as you would whole numbers Count total number of decimal places in multiplier and number to be multiplied Starting on right of product, count number of decimal places from previous step Always count places from right to left

Multiplying by Power of 10 Move decimal one place to the right for each zero in the multiplier Example: 0.5 x 10 = 5.0 Example: 0.5 x 100 = 50.0 Example: 0.5 x 1,000 = 500.0

Dividing Decimals by Whole Numbers Place decimal point in quotient directly over decimal point in dividend Divide dividend by divisor Double-check accuracy by multiplying quotient by divisor (answer equals dividend)

When the Divisor Is Larger Than the Dividend Place decimal point in quotient on answer line above decimal point in dividend Place zero (0) before decimal point (continues)

When the Divisor Is Larger Than the Dividend If whole number will not go into first number, place a zero (0) immediately after decimal point Continue placing zeros until you are able to divide the numbers

Dividing Whole Numbers by Decimals Place decimal point at the end of the whole number of the dividend Place a zero after the decimal point Move the decimal point to the end of the divisor (continues)

Dividing Whole Numbers by Decimals Move the decimal point the same number of places to the right in the dividend that you moved it in the divisor Divide as usual

Dividing Decimals by Decimals Make divisor a whole number by moving the decimal point to the right Move the decimal point the same number of spaces in the dividend that you did in the divisor (continues)

Dividing Decimals by Decimals Place a decimal point on the answer line above the new decimal point in the dividend Place a zero before the marked-off decimal point Divide as usual

Percentage Percent: “per hundred” Whole numbers are expressed as 100% % = denominator of 100 Percent indicates parts of a whole To express percents as fractions, remove the percent sign and write as numerator of fraction with denominator of 100 Example: 75% = 75/100 (continues)

Percentage If percent is mixed number, numerator is divided by 100 Example: 1.5% = 150/100 To express fractions as percents, multiply by 100 and add the percent sign Example: 3/4 = 75%

Quantity of Percents Express percent as a decimal or fraction Multiply whole number by decimal or fraction Example: How much is 10% of 80? 10% = 0.10 = 10/100 or 1/10 80 x 0.10 = 8.0 80 x 1/10 = 8